Adding Global Groups to Domain Local through script.

Hi, I have a script from creating Local Domain groups from Global Security groups, now I want to expand that script so it automatically adds that Global group to Domain Local group.

Here is the script that I have and that works for creating Domain Local groups:

$groups = Get-ADGroup `
    -Filter 'GroupScope -eq "Global" -and GroupCategory -eq "Security"' `
    -Properties Description,DisplayName,ManagedBy
ForEach ($group in $groups) {
    
    $params = @{
        Path = $group.DistinguishedName -replace '^cn=.+?(?<!\\),'
        Name = "DL_FGL_$($group.Name)"
        SamAccountName = "DL_$($group.SamAccountName)"
        Description = "$($group.Description)"
        DisplayName = "$($group.DisplayName)"
        ManagedBy = $group.ManagedBy
        GroupCategory = "Security"
        GroupScope = "DomainLocal"
    }
    Try {
        Get-ADGroup -Identity "DL_$($group.SamAccountName)" | Out-Null
    }
    Catch {
        New-ADGroup @params
    }
}